One of the biggest challenges we’ve faced this year is what to do with our “final exam”.  Our mostly traditional math department has always had cumulative and shared final exams where students cram material to show their teachers how much of the year’s work they have retainou caned.  This was always interesting to me since I never really understood the point this type of final exam.  Does learning mathematics mean that you are able to repeat material that you learned nine months ago? Does it mean that you can study very hard and remember how to do problems becasue you’ve memorized the process?  Or does it mean that you have a certain bank of skills and concepts that you can access in order to solve problems given to you?

We geometry teachers agreed with my last definition of the purpose of a “final exam”.  We felt that if we were really teaching this course towards better problem solving skills for students, we better find a way to emulate that experience for the students in order to most authentically assess their problem solving skills.  This was a daunting task and a very difficult one to craft.

What we decided to do was create a situation most like the problem sets they had done for us all year, but also to emulate the classroom environment of discussion and sharing of ideas in order to best assess their independent and group problem solving skills.  The first piece of this was to come up with five problems that we thought were challenging enough for a group to take on, but at the same time included skills and concepts that were threaded through the curriculum throughout the year.  Students were allowed to use their journals, which served as their resource throughout the year as well.

But how to replicate the classroom environment?  We decided to construct groups that would be well-balanced with respect to ability, in order to see these students work together and use their skills.  Assessing that type of work proved to be very difficult indeed.  The teachers walked around and attempted to observe students in their classes and rated them on how well they:

  • Listen well to others
  • Focus on Task
  • Participate in Discussion
  • Productively discuss ideas
  • Help others understand
  • Contribute to the solution. 

Not only did the teachers assess each student in their section, but we had each group members assess the others in their group.  The average rating in each category (1-5) was then added up for a total number of points out of 30.  This percentage then counted as 50% of their final exam grade, with the other 50% being the points for the 5 written solutions solved as a group.

In retrospect, it may have been a slightly-less-than-perfect model to use, but we were glad we tried it.  Some problems that arose were that a few groups (2 or 3 out of 16) did not take this rating system seriously and the teachers were forced to balance their scores with the students’.  We also found that there was so much feedback about how the groups worked together that it was difficult to accurately score how a certain individual did.  Interestingly, some students did feel comfortable writing their comments on the sheet we gave them and one emailed us an explanation of her scoring later that day.  Some ideas for next year would be to have 2-3 questions done as a group and 2-3 questions done as individuals and see if that worked out more fairly.

Overall, I am proud of my colleagues who trired something different, but extremely deliberate.  We tried to model for the students the classroom process that we held so important all year long.  For that, I feel that it was authentic, even if we learned a great deal from it as well.